Positive Periodic Solutions For A Class Of Nonlinear Functional Differential Equations

In this paper, we study the problem on the existence of positive periodic solutions for a class of nonlinear functional equations. In Chapter 2, we study the problem on the existence of positive periodic solutions for the equationsx'(t) = -a(t)x(t) + f(t,x(t-τ1(t,x(t))),… ,x(t-τm(t,x(t)))), (1)x'(t) = a(t)x(t) - f(t, x{t -τ1(t, x(t))),… ,x(t- τm(t, x(t)))). (2)By constructing a completely continuous operator in a functional space and employing the cone compression and expansion fixed point theorems, we obtain some sufficient conditions which guarantee the existence of positive periodic solutions for Eq. (1) and (2). The obtained results improve the ones of papers [1] and [6].In Chapter 3, we study the problem on the existence of multiple positive periodic solutions of the equationsx'(t) = -a(t,x(t))x(t) + f(t,x(t - τ1(t,x(t))),… ,x(t-τm(t,x(t)))), (3)x'(t) = a(t,x(t))x(t) - f(t,x(t -τ1(t,x(t))),… ,x(t - τm(t,x(t)))). (4)By constructing a completely continuous operator in a functional space and employing some fixed point theorems, we obtain some new results which guarantee the existence of multiple positive periodic solutions of the Eq. (3) and (4). The results obtained improve the ones in the paper [8].